\section{Quantifications}
Energy variables like wind and solar production are known to be largely affected by meteorological configurations, with more unstable conditions favouring the former, while solar typically benefitting from dry environments. Besides, power demand correlates with temperature-related factors, again driven by these large scale systems.
Hence, we first focus on the average configurations led by regimes in the different European countries.

\begin{figure}[!htbp]
    \centering
    \begin{subfigure}{.32\textwidth}
    \centering
    \includegraphics[width =\textwidth]{imgs/wind_anomaly_EU7.png}
    %\caption{Wind Load Factor Deviation (\%) under the different regimes for EU-7 countries}
    \end{subfigure}
    \hfill
    \begin{subfigure}{.32\textwidth}
    \centering
    \includegraphics[width =\textwidth]{imgs/solar_anomaly_EU7.png}
    %\caption{Solar Load Factor Deviation (\%) under the different regimes for EU-7 countries}
    \end{subfigure}
    \hfill
    \begin{subfigure}{.32\textwidth}
    \centering
    \includegraphics[width =\textwidth]{imgs/load_EU7.png}
    %\caption{Power Demand (GW) during business days under the different regimes for EU-7 countries}
    \end{subfigure}
    \caption{Wind Load Factor Deviation (\%) (left), Solar Load Factor Deviation (\%) (center), Power Demand (GW) during business days (right) under the different regimes for EU-7 countries}
    \label{fig:inter_EU7}
\end{figure}
\begin{figure}[!htbp]
    \centering
    \begin{subfigure}{\textwidth}
    \centering
    \includegraphics[width =\textwidth]{imgs/maps_Wind Load Factor_regimes.png}
    \caption{Wind Load Factor Deviation (\%) under the different regimes for EU-7 countries: a geographic visualization}
    \end{subfigure}
    \hfill
    \begin{subfigure}{\textwidth}
    \centering
    \includegraphics[width =\textwidth]{imgs/maps_Load_regimes.png}
    \caption{Power Demand Deviation (\%) under the different regimes for EU-7 countries: a geographic visualization}
    \end{subfigure}
    \caption{Geographic visualization of the regimes and countries relationships of the Wind Load Factor and Power Demand variables}
    \label{fig:inter_EU7_maps}
\end{figure}

The results we obtain are reported by Figures \ref{fig:inter_EU7}, \ref{fig:inter_EU7_maps}, and show very distinct behaviors that can be summarized as:
\begin{itemize}
    \item Southern European countries (Italy and Spain) generally undergo to different setups, having milder conditions than Northern and Central countries
    \item Wind: the generally unstable conditions of NAO+ lead to much above normal productions of wind power plants, while Scandinavian Blocking (an usual dry regime) negatively affects how wind power plants can satisfy the power demand of a country. Further, Germany (GE) benefits from a regime like AR, generally leading to around normal winds. NAO-, instead, is a regime leading to cold temperatures and relatively dry meteorological setups. It is thus justified to have evidence of below normal productions
    \item Solar: being almost mutually exclusive with wind, data reflects an opposite situation. Here, SB is in average the regime under which production is boosted, whereas instead NAO+ ranks as the worst configuration. However, it is worth to notice that the magnitude of the deviations is much lower, clearly denoting the minor variability of this energy source
    \item Load: we analyze power demand on business days, since the effects of the industrial sectors can be taken into account. The statistics explicit an empirical trend widely discussed in meteorology: the presence of high wind and unstable conditions is usually associated with warmer temperatures. Indeed, NAO+ clearly reduces the overall power demand of a country, whose only sources of variability during weekdays are the private energy consumptions (in winter, heating systems). AR, NAO- and SB are instead similarly cold during winter, with the exception of southern countries under NAO- benefitting from more temperate climates
\end{itemize}
Collecting this fine-grained information is of uttermost importance, since it implicitly hides financial strategies in the energy markets. Recalling Figure \ref{fig:price_elec}, electricity prices are largely affected by how much demand can be satisfied by low-cost energy sources. Hence, we could expect that, under NAO+, extremely positive wind productions would likely lower the overall price, eventually allowing to keep gas and coal plants off. Instead, SB, although being favourable for Solar, should lead to higher price values due to the lack of wind.\\
\begin{figure}[!htbp]
    \centering
    \includegraphics[width = \textwidth]{imgs/WindSolarGE.png}
    \caption{Example of historical distributions of the Wind and Solar Load Factor energy variables, isolated to an individual country (Germany)}
    \label{fig:intra_country}
\end{figure}

As a next step, we recreate the distributions of many energy variables in the context of individual countries, to understand their statistical properties, and to assess a more faithful quantification. We are able to do this, considering the aforementioned historical series of measurements on the grid by the respective national operators. As an example, Figure \ref{fig:intra_country} shows some insight into the distribution of the utilization of windy and solar power plants in Germany. Again, we are able to establish a bound on the maximum expected production from the two energy sources, by just considering what kind of events happened in history, and what was their intensity. For example, NAO+ and AR in Germany are comparable in their distribution, while NAO-, while largely variable, is generally less productive; SB is instead limited even in those days presenting an outlier behavior, suggesting a bearish trend in wind production. For the Solar counterpart, as outlined previously, variability is much more contained for most of the regimes, while clearly evidencing the benefits brought by the Blocking regime.

\begin{figure}[!htbp]
    \centering
    \includegraphics[width = \textwidth]{imgs/WindSolarGEMonth.png}
    \caption{Example of monthly historical distributions of the Wind and Solar Load Factor energy variables, isolated to an individual country (Germany)}
    \label{fig:intra_country_month}
\end{figure}
Diving deeper at a monthly level (Figure \ref{fig:intra_country_month}), we notice how January has a negative impact on the wind production under the NAOs and AR regimes. The explanation to this event can be found in an atmospheric phenomenon, usually happening at the beginning of the month: the Polar Vortex disruption. Its frequency is not yearly, but when it occurs, wind events are typically milder than usual, and NAO- becomes the prominent regime for longer-than-average periods.\\
The only noticeable effect of Solar is instead the progressive increasing of the utilization factor as moving out from the winter season.\\
Finally, we perform a thorough analysis of extreme meteorological events in relation to weather regimes. We define an event as ``extreme'' in all those cases it falls beyond the 98th percentile of the distribution. Knowing which regimes are more likely to create disruptions is of paramount importance in that it allows to predict huge volatilities in energy markets. The results we collect are reported in Figure \ref{fig:extreme_events}.
\begin{figure}[!htbp]
    \centering
    \begin{subfigure}{.48\textwidth}
    \centering
    \includegraphics[width = \textwidth]{imgs/WindExtreme.png}
    \end{subfigure}
    \hfill
    \begin{subfigure}{.48\textwidth}
    \centering
    \includegraphics[width = \textwidth]{imgs/LoadExtreme.png}
    \end{subfigure}
    \caption{Occurrence (\%) of extreme events in EU-7 countries in the four different regimes for Wind (left) and Power Demand (right)}
    \label{fig:extreme_events}
\end{figure}